Norton is a bit of a pig to remove even after an uninstall (a must) remnants might remain.
A link worth looking at, which is a program removal tool that can remove the remnants of a number of different Norton Programs:
Removing your Norton program using SymNRTThat is a possible for a Red circle over the a icon but not normally associated with no icon at all. That is usually down to other security applications, like those mentioned below that monitor new startup entries like the one for ashDisp.exe (the icon and interface to the on-access protection).
What other security based software do you have that might block new startup entries, e.g. Spybot S&D (TeaTimer), AdAware (AdWatch), SpySweeper, Spyware Doctor (StartUpGuard or OnGuard), PrevX, WinPatrol, ProcessGuard, etc. ?
avast! icon missing - As a temporary measure until this is resolved you can create a desktop shortcut for this file C:\Program Files\Alwil Software\Avast4\ashDisp.exe (the avast icon and interface to the providers). Right click on the file and select Send To, Desktop (create shortcut). You will need to run this after each boot until the problem is resolved.
Or Make a link to ashdisp.exe in your startup folder.
The above options you should only investigate having uninstalling Norton and running the Norton uninstall tool.